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3 years ago

To solve 5(2^x + 4) = 15...

Mathematics

1 answer:

horrorfan [7]3 years ago

5 0

I don't think you need answer for that you already did it.

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Find the angles between -pi and pi that satisfy:<br><br> (−√3) sin(v)+cos(v)=√3

MAXImum [283]

Observe that

$\sin\left(\dfrac\pi6-v\right)=\sin\dfrac\pi6\cos v-\cos\dfrac\pi6\sin v=\dfrac12\cos v-\dfrac{\sqrt3}2\sin v$

In the original equation, divide both sides by $\dfrac12$ :

$-\sqrt3\sin v+\cos v=\sqrt3\implies\dfrac12\cos v-\dfrac{\sqrt3}2\sin v=\dfrac{\sqrt3}2$

$\implies\sin\left(\dfrac\pi6-v\right)=\dfrac{\sqrt3}2$

Next,

$\sin x=\dfrac{\sqrt3}2\implies x=\dfrac\pi3+2n\pi,x=\dfrac{2\pi}3+2n\pi$

where $n$ is any integer. Then

$\sin\left(\dfrac\pi6-v\right)\implies v=-\dfrac\pi6-2n\pi,v=-\dfrac\pi2-2n\pi$

Fix $n=0$ to ensure $-\pi$ , so that

$v=-\dfrac\pi6,v=-\dfrac\pi2$

3 0

4 years ago

One cubic meter of water weighs approximately 2200 pounds. There are 100 cm in one meter. If you have a box-shaped fish tank tha

Diano4ka-milaya [45]

Answer:

158.4 pounds

Step-by-step explanation:

first find the volume of the tank

$V = 30 \times 30 \times 80$

$V = 72000 cm^3$

to convert this to m^3 we know that 1m = 100cm

$V = 72000 cm^3 \times \left(\dfrac{1\,\text{m}}{100\,\text{cm}}\right)^3$

$V = 72000 cm^3 \times \left(\dfrac{1\,\text{m}^3}{100^3\,\text{cm}^3}\right)$

the cm^3 cancel out.

$V = \dfrac{72000}{100^3} m^3$

$V = 0.072\,m^3$

by simply converting the side-lengths to meters beforehand can give you this answer directly:

$V = 0.3 \times 0.3 \times 0.8 = 0.072 m^3$

it is given that 1 meter cube of water weighs about 2200 pounds.

$1\,m^3 = 2200 \,\text{lb}$

multiply both sides with 0.072 to find our answer:

$1\,m^3 \times 0.072 = 2200 \times 0.072 \,\text{lb}$

$0.072\,m^3 = 158.4 \,\text{lb}$

hence the weight of the water in the tank would be 158.4 pounds!

3 0

3 years ago

A_____ function is a function that can be expressed as the quotient of two polynomial functions in wich the denominator does not

Korolek [52]

Answer:

rational

Step-by-step explanation:

that is literally the definition of a rational number, just change the part where it says function to number and polynomial functions to number as well.

4 0

3 years ago

It is given that R=2q-5 and Q=3p+2. Find the numerical value of R when p=3

saveliy_v [14]

Answer:

R = 17

Step-by-step explanation:

R = 2q - 5

Q = 3p + 2

Find the numerical value of R when p = 3

R = 2q - 5

R = 2(3p + 2) - 5

R = 6p + 4 - 5

R = 6p - 1

When p = 3

R = 6(3) - 1

R = 18 - 1

R = 17

4 0

3 years ago

What is the equation in standard form of the line y = 1/9x + 5?

patriot [66]

Answer:

the standard form of equation is in the form of

x - 9y = -45 , so the answer is B

7 0

3 years ago

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